If POA, would that give me authorization to decide what medication my mom takes?

No. Your job is not to micromanage someone else's life. It's simply an "overseer" kind of thing, set up when a person can no longer take care of their financial or personal affairs.
The term is used pretty loosy-goosy around here and I honestly don't KNOW what each individual interprets it to be. For legal clarification, look it up.

Here is a good explanation of documents that authorize making medical decisions:
https://www.agingcare.com/articles/legal-documents-to-make-healthcare-decisions-for-your-parent-146623.htm

I would want this to be a decision made with a doctor.

No. The person with medical POA (healthcare proxy) has that authority if Mom is no longer competent to make her own decisions.

Are you a physician?